determine an equation and the radius for the circle that has its centre at the origin (0,0) passes through the point A 4-3

Determine An Equation And The Radius For The Circle That Has Its Centre At The Origin (0,0) Passes Through

Answers

Answer 1

Given:

The center of the circle is at (0,0).

The circle passes through the point A(4,-3).

To find:

The radius and the equation of the circle.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The radius of the circle is the distance between the points (0,0) and (4,-3).

[tex]r=\sqrt{(4-0)^2+(-3-0)^2}[/tex]

[tex]r=\sqrt{(4)^2+(-3)^2}[/tex]

[tex]r=\sqrt{16+9}[/tex]

[tex]r=\sqrt{25}[/tex]

[tex]r=5[/tex]

So, the radius of the circle is 5 units.

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where, (h,k) is center of circle and r is the radius.

Putting h=0, k=0, r=5, we get

[tex](x-0)^2+(y-0)^2=5^2[/tex]

[tex]x^2+y^2=25[/tex]

Therefore, the radius of the circle is 5 units and the equation of the circle is [tex]x^2+y^2=25[/tex].


Related Questions

In ARST, r = 52 cm, s = 55 cm and ZT=48°. Find the length of t, to the nearest
centimeter.

Answers

9514 1404 393

Answer:

  44 cm

Step-by-step explanation:

The law of cosines is applicable.

  t^2 = r^2 + s^2 -2rs·cos(T)

  t^2 = 52^2 +55^2 -2·52·55·cos(48°) ≈ 1901.57

  t ≈ √1901.57 ≈ 43.607

The length of t is about 44 cm.

Hey there!

[tex]\dagger \: \sf\red{Question:}[/tex]

In ARST, r = 52cm, s = 55cm and ZT = 48°. Find the length of T, to the nearest centimeter.

[tex]\dagger \: \sf\blue{Solution:}[/tex]

By the law of cosines,

[tex]{\underline{\boxed{\frak{\pmb{\quad {t}^{2} = {r}^{2} + {s}^{2} - 2rs \times cos(T) }}}}} [/tex]

[tex]\implies\tt[/tex] t² = (52)² + (55)² - 2 × 52 × 55 × cos(48°)

[tex]\implies\tt[/tex] t² ≈ 1901.57

[tex]\implies\tt[/tex] t² = √1901.57

[tex]\implies\tt[/tex] t² = 43.607

[tex]\implies\tt[/tex]t = 44 cm

Therefore;

The length of t is 44 cm.

Charlie Fox's Pizza has a coupon for 30% off an extra large pizza. If the pizza you want
regularly costs $28, how much would the sale price be?

Answers

Answer:

8.4

Step-by-step explanation:

Move the decimal point to create $2.8, which is 10% of $28. Once you have the 10% ($2.8) multiply it by 3 to get 30%.

3 (t + 4) = 25.5

t= ??

Answers

Answer:

t = 4.5

Step-by-step explanation:

Distribute 3 to the parentheses:

3(t + 4) = 25.5

3t + 12 = 25.5

Subtract 12 from both sides:

3t = 13.5

t = 4.5

So, the answer is t = 4.5

I need help on this question.

Answers

The correct answer is C.

find the size of angle x.

Answers

You need to subtract. From 180 and the other number so subtract 180
- 124
And you will get your answer. I hope this helps.

Express 150 as:
a) A fraction of 350.
b) A percentage of 600.

Answers

A) 3/7 and B) 25%. Give me a like if I helped please :)

Answer:

a)3/7

b)25%

Step-by-step explanation:

PLEASE HELP!! 50 POINTS!
Answer the question in the picture.

Answers

Answer:

1.9

2.16

3.225

4.196

5.25

6.256

I answered again since they deleted mine

1.9

2.16

3.225

4.196

5.25

6.256

hope it helps

Please give me the correct answer.​

Answers

Answer:

The rate of change is 2 euros.

Step-by-step explanation:

You can see on the graph the cost goes up 2 euros each hour. Hope this helps!

It’s 2 1:14 1:16
16-14 =2
Then same things for every other number/ratio
Rate of change = 2

Can someone help me with this geometry question ASAP ty

Answers

Answer:

angle S    100  option C

Step-by-step explanation:

P and S are consecutive angles

Interior angles of a parallelogram

1. Opposite angles are congruent

2. Consecutive angles are supplementary (They add to 180 )

(2x+20) + (3x+10) = 180

5x+30 = 180

5x = 150

x= 30

angle S      3x30 +10 =

                   90 +10 =   100

The other angle P      2x30 +20 = 60 +20 = 80

  100 +80 = 180

 

What’s equivalent to 5(2x+6)

Answers

Answer:

5(6+2x)

Step-by-step explanation:

2.08/4

i also need a explanation on it

Answers

Answer:

0.52

Step-by-step explanation:

First, I would do 2 divided by 4 is 0.5. Then I would do 0.08 divided by 4 and get 0.02. Finally, I would add 0.5 and 0.02 and get 0.52.

how many cats can fit in one box?

Answers

Answer:

depends on how big the box and cats are

Step-by-step explanation:

well it defends on how big or small the box is

William is planning to cover one side of the roof of his barn with solar panels.
The part of the roof he plans to cover is 12 feet by 30 feet, and each solar panel is
encased in a frame that is 16 inches by 20 inches. What is the minimum number
of solar panels that William will need to purchase to completely cover this part
of his roof?
I

Answers

Answer:

5 i think

Step-by-step explanation:

to start you need to find the total area the side of the roof he plans to cover which is 360 feet.

16x2 + 20x2 = 72

so lets just say thats the total area of one solar panel then you could just divide 360 feet by 72 feet to get...

5. so i guess william needs 5 solar panels

i could be spouting nonsense rn.. so sorry if im wrong

John is making a circular table that has a top with a diameter of 24 inches. Find the circumference of the table and round to the nearest tenth.

Answers

Answer:

The cirumference would be 78.5.

24*pi would equal 75.5398163397 so just round that.

Hope this helped

please help me its my plato grade

Answers

Answer:

C)

Step-by-step explanation:

because the graph has been translated 5 units to the left and one unit down, and C matches the requirements

Someone help please hurry and make sure is right :)

Answers

Answer:

Corresponding

Step-by-step explanation:

x and y are corresponding angles.

That is a corresponding angle

the diameter of a circle is 14m. find the circumference to the nearest tenth​

Answers

Answer:

44

Step By Step Explanation:

Formula for circumference - 2πr

1. Find raduis: 14/2=7 - Radius=7

2. Plugin number and solve - 2π(7)=43.9822971503

3. Round 43.9822971503 to 44.

how do i solve this question 2+3=8-4 ?

Answers

Answer:

5=4

Step-by-step explanation:

5=4

just add then subtract

Which expression is equivalent to 6(5x + 4) - 6x ?
a. 24x + 24
b. 48x
C. 30x + 24
d. 5x + 10​

Answers

Answer:

a. 24x + 24

Step-by-step explanation:

Given

6(5x + 4) - 6x

= 30x + 24 - 6x

= 24x + 24

Hope it will help :)❤

what is this ????????????????

Answers

Answer:

(2-3)

Step-by-step explanation:

What is the value of x in the equation 0.03x − 1.2 = 0.24?

Answers

Answer:

x = 48

Step-by-step explanation:

solved it just now-

uh help hereeeee pls.

Answers

Answer:

d.PS

Step-by-step explanation:

option D,line PS is opposite

what is the ratios to 25:90

Answers

Answer:

5/18

Step-by-step explanation:

25 / 90 =5*5 / 5*18 =5/18

Decide whether each expression simplifies to a number less than -1 or greater than 1.

Less than -1
Greater than 1
Neither


(-10) divided by 6
-(5 divided by 2)
-3 divided by (-4)
-2• [- 7/2]
8/3•[-3:5]

Answers

Answer:

Step-by-step explanation:

(-10) ÷ 6 = [tex]\frac{-10}{6}=\frac{-5}{3}=-1\frac{2}{3}[/tex]   less than -1

-(5÷2) =[tex]-\frac{5}{2}=-2\frac{1}{2}[/tex]    less than (-1)

(-3÷ (-4) = [tex]\frac{-3}{-4}=\frac{3}{4}[/tex]   Neither

(-2)* [-7/2] = [tex](-2)* \frac{-7}{2}=(-1)*(-7)=7[/tex] Neither

(8/3)*(-3/5)=[tex]\frac{8}{3}*\frac{-3}{5}=\frac{-8}{5}=-1\frac{3}{5}[/tex]     less than (-1)

what is the value of x ? ​

Answers

Answer:

97 degrees

Step-by-step explanation:

360 degrees is our total. so:

306 - 60 - 30 - 72 - 46 - 55 = x

x = 97

Which is an equivalent expression written using Distributive property: 3 (m + 3)

Answers

Answer:

3m + 9

Step-by-step explanation:

please could u help me with this?​

Answers

43.68. You multiply the base by the height

A principal of $3400 is invested at 4.75% interest, compounded annually. How much will the investment be worth after 5 years?
Use the calculator provided and round your answer to the nearest dollar.

Answers

Answer:

4287.94

Step-by-step explanation:

the equation would be 3400(1+4.75)^5 which equals to 4287.94

42.987 jendbjdjdndbshhs

Whats the perimeter?

Answers

Answer: The perimeter is 40.1

Step-by-step explanation: This is because a perimeter is just all the sides added up so 8+4+4+4.5+5.6+14 which is 40.1

Hope this helps and have a nice day

Answer:

The perimeter is 40.1

Step-by-step explanation: This is because a perimeter is just all the sides added up so 8+4+4+4.5+5.6+14 which is 40.1

Hope this helps and have a nice day

Step-by-step explanation:

okay heres the photo

Answers

Anwser = 117


Hope it helped
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